Encyclopaedia of DesignTheory:
A polarity

For each cell (i,j), the set of 6 cells lying either in
row ior in column jbut not both is a block;
and these are all the blocks.

The table shows block (2,3).

Two points in the same row, such as (1,1) and (1,2), lie in the two blocks
(1,3) and (1,4); similarly for points in the same column;
and two points in different rows and columns, such as (1,1)
and (2,2), lie in the two blocks (1,2) and (2,1). The design is thus balanced
with lambda=2, as claimed.

Now it is clear that if the point (i,j) is incident with the block
labelled by (k,l), then the point (k,l) is incident with the
block labelled by (i,j). (This happens if and only if i=k or
j=l but not both.)

So the correspondence which interchanges each point with the block having the
same label is a polarity of the design.

Moreover, this polarity has no absolute points. So there is a corresponding
(16,6,2) graph (that is, a strongly regular graph with v=16,
k=6, and lambda=mu=2), whose vertices are the cells,
joined if they lie in the same row or column. This is the square lattice
graph L2(4).

Remarkably, the design has a different polarity with no points absolute, for
which the (16,6,2) graph is the Shrikhande graph; and also a polarity with
every point absolute, associated with the Clebsch graph.